In a large oven-safe skillet, melt 2 tablespoons of unsalted butter and 1 tablespoon of olive oil over medium-low heat. Add 2 large sliced yellow onions, a teaspoon of sugar, and a pinch of salt. Cook for 30 to 40 minutes, stirring frequently until the onions are a deep golden brown and caramelized. Stir in 3 minced garlic cloves in the final minute.

Season 2 cups of cooked shredded chicken with salt and pepper. In a separate skillet, heat a dash of oil over medium heat. Brown the chicken pieces on each side for about 3-4 minutes. Remove from heat and set aside.

Pour 2 cups of low-sodium beef broth into the pan with the caramelized onions, scraping up any browned bits. Stir in 1.5 cups of orzo pasta, 1 cup of heavy cream, and 0.5 teaspoon of dried thyme. Add the browned chicken and bring to simmer. Cook for 5-7 minutes.

Preheat your oven to 375°F (190°C). Stir half of the 1.5 cups of shredded mozzarella cheese into the mixture until melted. Transfer to the oven, top with remaining mozzarella and sprinkle with grated Parmesan cheese. Bake for 20-25 minutes until the top is bubbly and golden.

Remove from oven and let rest for 5-10 minutes. Garnish with fresh thyme or parsley. Serve warm.